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proposed

<a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,5,-3,1).

G.f.: (x^7-3*x^6+3*x^5-2*x^4+x^3-3*x^2+3*x-1)/((x^3-x^2+2*x-1)*(x-1)^2). - Alois P. Heinz, Feb 10 2019

nonn,more,easy,changed

More terms from Alois P. Heinz, Feb 10 2019

1, 1, 1, 2, 6, 12, 23, 44, 82, 149, 267, 475, 841, 1484, 2613, 4595, 8074, 14180, 24896, 43702, 76705, 134622, 236260, 414623, 727629, 1276917, 2240851, 3932438, 6900967, 12110373, 21252244, 37295110, 65448378, 114853920, 201554603, 353703696, 620706742

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editing

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Cf. A000325, A001610, A001680, A005251, A066982, A306351, A323950, A323951, A323952, A323954.

Cf. A306351, A323950, A323951, A323952, A323954.

1, 1, 1, 2, 6, 12, 23, 44, 82, 149, 267, 475, 841, 1484, 2613, 4595, 8074, 14180, 24896, 43702, 76705, 134622, 236260, 414623, 727629, 1276917

allocated for Gus WisemanNumber of ways to split an n-cycle into connected subgraphs, none having exactly two vertices.

1, 1, 1, 2, 6, 12, 23, 44, 82, 149, 267, 475, 841, 1484, 2613, 4595, 8074, 14180, 24896, 43702, 76705

0,4

The a(1) = 1 through a(5) = 12 partitions:

{{1}} {{1}{2}} {{123}} {{1234}} {{12345}}

{{1}{2}{3}} {{1}{234}} {{1}{2345}}

{{123}{4}} {{1234}{5}}

{{124}{3}} {{1235}{4}}

{{134}{2}} {{1245}{3}}

{{1}{2}{3}{4}} {{1345}{2}}

{{1}{2}{345}}

{{1}{234}{5}}

{{123}{4}{5}}

{{125}{3}{4}}

{{145}{2}{3}}

{{1}{2}{3}{4}{5}}

cyceds[n_, k_]:=Union[Sort/@Join@@Table[1+Mod[Range[i, j]-1, n], {i, n}, {j, Prepend[Range[i+k, n+i-1], i]}]];

spsu[_, {}]:={{}}; spsu[foo_, set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@spsu[Select[foo, Complement[#, Complement[set, s]]=={}&], Complement[set, s]]]/@Cases[foo, {i, ___}];

Table[Length[spsu[cyceds[n, 2], Range[n]]], {n, 15}]

Cf. A000325, A001610, A001680, A005251, A066982.

Cf. A306351, A323950, A323951, A323952, A323954.

allocated

nonn,more

Gus Wiseman, Feb 10 2019

approved

editing

allocated for Gus Wiseman

allocated

approved